Bayesian Modeling of the Equation of State for Liquid Iron in Earth's Outer Core

Abstract

We use Bayesian modeling of the equation of state (EoS) to constrain the density (ρ) and P wave velocity (VP) of liquid iron under conditions of Earth's outer core. Experiments at such high pressures (P) and temperatures (T) are technically challenging, so there are few data available to use in parameter optimization of the EoS. Our Bayesian inference modeling successfully estimates the posterior probability distribution of the parameters and unobserved data by using the Hamiltonian Monte Carlo method. These posterior probability distributions allow calculation of P-ρ and P-VP profiles of liquid iron along the adiabatic P-T profile together with the associated credible intervals. Assuming that the temperature at the core-mantle boundary (CMB) is 3,500–4,200 K, the P-ρ and P-VP profiles show deviations of ρ and VP from the preliminary reference Earth model of about 8–11% and −3% to −5%, respectively. Deviations of the 95% credible intervals of the P-ρ profile for the CMB and the inner core boundary are 6.9–9.7% and 6.5–9.8%, respectively. Equivalent deviations of the P-VP profile are −4.8% to −1.5% and −6.0% to −2.3%, respectively. Bayesian modeling of the EoS enables integration of small data sets that include unobserved data and evaluation of uncertainty ranges of physical properties, such as ρ and VP, which are essential for comparison with seismological properties of the core.